The World Cup winner is understood to have held talks with Marseille recently, but according to the 'Daily Mail', he is keen to fight for his place with the 'Blues'.
Giroud only joined Chelsea from Arsenal in January as he registered figures of 12 goals in 44 games in all competitions between the two sides.
The former Montpellier man played in all seven of France's World Cup games in Russia, but failed to score a single goal.
Nevertheless, there has been plenty of reported interest in Giroud, with Atletico Madrid and Marseille among the sides linked in the press.
Maurizio Sarri's desire to bring Gonzalo Higuain to the Bridge would appear to be the final nail in the coffin for Giroud, who already has Alvaro Morata, Michy Batshuayi and Tammy Abraham to compete with up front.
However, the experienced target man seemingly remains confident of proving his worth to the side.